Deriving Model Parameters

A specific model incorporating a state-variable approach was used to predict soil organic carbon under different conditions. The model was based on the concept of buildup and breakdown processes that depend on the soil organic carbon content of the system. The soil organic carbon build-up rate (R) was described by the following mathematical function:

Figure 20.2 Soils of Uganda. (Data from Food and Agriculture Organization. 1998. The Soil and Terrain Database for Northeastern Africa: Crop Production System Zones of IGAD Sub Region. FAO Land and Water Digital Media Series 2. Food and Agricultural Organization, Rome. Map courtesy of Development Ecology Information Service, Alexandria, VA.)

Table 20.2 Soil Organic Carbon (0- to 15-cm Depth) in Various Land Uses Across Major Agroclimatic Zones in Uganda

Soil Organic

Table 20.2 Soil Organic Carbon (0- to 15-cm Depth) in Various Land Uses Across Major Agroclimatic Zones in Uganda

where g is the relative soil organic carbon buildup rate (yr-1), C is the soil organic carbon content (%) at time t, and Cmax is the maximum attainable soil organic carbon content (%). Equation 20.1 implies that soil organic carbon buildup is exponential when soil organic carbon content is very small compared to Cmax, and maximum R = g when soil organic carbon tends to zero. The rate of soil organic carbon buildup reduces and tends to zero as C tends to Cmax. The rate of soil organic carbon breakdown (L) was described by the following function:

where Lmax is the maximum attainable soil organic carbon loss rate (yr-1), Cr is the minimum/passive soil organic carbon content (%), Cs is shape factor of the function, and C is the soil organic carbon content (%) at time t. Cr represents the minimum protected soil organic carbon beyond which further breakdown of soil organic carbon is not significant. The breakdown rate (L) is highest when soil organic carbon content is maximum. The soil organic carbon sequestration over time per unit soil organic carbon content is the difference between the rate of buildup (R) and breakdown (L), and is described by the function ddC = (R - L) C (20.3)

dt where C is the soil organic carbon content (%) at a time t.

The soil organic carbon content (area between the two functions) was then obtained by the analytical integration of Equation 20.3; thus,